Turing Machine Visual Guide

Formal Definition of a Turing Machine

M = (Q, Σ, Γ, δ, q₀, ␣, F)

Q

Finite set of states (control unit states)

q₀ q₀

→

q₁

→

qf qf

Σ, Γ

Σ: Input alphabet (e.g., {0, 1})

Γ: Tape alphabet (Σ ⊆ Γ - {␣})

0

1

␣

X

Y

δ

Transition function:

Q × Γ → Q × Γ × {L, R}

δ(q0, 0) = (q1, 1, R)

If in q0 reading 0, go to q1, write 1, move right

q₀

Initial state where computation begins

␣

Blank symbol (not in Σ, part of Γ)

F

Set of final/accepting states (F ⊆ Q)

Turing Machine Operation

Tape Visualization

Current State: q₀

Instantaneous Description: q₀ 0 1 0

Control Panel

Input String

Speed

Transition Table

Current State	Read Symbol	New State	Write Symbol	Move

Step-by-Step Operation

1

Initialization

The machine starts in state q₀ with the input string on the tape, surrounded by blanks (␣). The head is positioned at the leftmost input symbol.

2

Read Symbol

The head reads the symbol at its current position. This symbol and the current state determine the next action.

3

Transition

The control unit consults δ (transition function) to determine: new state, symbol to write, and head movement direction.

4

Write & Move

The head writes the new symbol at its current position, then moves left (L) or right (R) one cell.

5

Repeat

Steps 2-4 repeat until no transition is defined for the current state and symbol (halt).

6

Accept/Reject

If halted in a final state (F), the input is accepted. Otherwise, it's rejected (either by halting in non-final state or infinite loop).

Instantaneous Description Example

The configuration of a TM at any point can be represented as: α q β

α: Tape contents to the left of the head
q: Current state
β: Tape contents at and to the right of the head

Initial: q₀ 0 1 0 ␣

After 1st transition: 1 q₁ 1 0 ␣

After 2nd transition: 1 0 q₁ 0 ␣

Final: 1 0 1 qf ␣ (Accepted)